以微觀力學模式模擬複合材料與應變率有關之非線性行為

Abstract

本研究目的在於以微觀力學模式描繪碳纖/環氧樹脂複合材料與應變率有關之非線性行為。材料性質方面，將環氧樹脂假設為彈性黏塑性材料並以三參數黏塑性模式描述之，纖維則假設為橫向等向性材料。藉由環氧樹脂在10E-4、10E-2以及1/s三種應變率之下的壓縮試驗，三參數模式所需的係數可藉由實驗獲得的應力應變曲線來定義。伴隨著已知的碳纖與環氧樹脂的材料性質，碳纖/環氧樹脂複合材料可藉由微觀力學模式進行模擬。在此研究中，有兩個微觀力學模式被採用，分別是Square Fiber Model以及Generalized Method of Cells。此外，兩種纖維排列方式（Square Edge Packing與Square Diagonal Packing）與兩種纖維形狀（圓形與正方形）被一併考量並且與ANSYS所執行之有限元素法做一系列纖維排列與纖維形狀對材料性質影響性的比較與探討。數值結果指出纖維形狀對偏軸複合材料機械性質的影響並不明顯，然而，纖維的排列方式對此卻有顯著的影響性，而且Square Edge Packing相較於Square Diagonal Packing模擬出更硬的應力應變曲線。 為了驗證微觀力學模式的準確性，偏軸的碳纖/樹脂複材試片在10E4到550/s的應變率之下做壓縮測試以獲得實驗值。由實驗值與模式預測的比較結果可知，數值預測結果雖然與實驗有一定程度的差異，但結合三參數黏塑性模式的微觀力學模式的確有能力描述與應變率有關的材料非線性行為。

This research aims to characterize the nonlinear rate dependent behavior of graphite/epoxy composites using a micromechanical approach. For epoxy phase, it was assumed to be following the elastic/viscoplastic behavior described by a three parameterts viscoplasticity model; while the graphite fiber was assumed to be a transverse isotropic solid. By performing compression tests on the epoxy resin at three different strain rates of 10E-4, 10E-2 and 1/s, the stress and strain relation of the epoxy resin was generated. Based on the experimental data, the three parameter viscoplasticity model was developed. With the ingredient properties, the mechanical behaviors of graphite/epoxy composites were characterized using the micromechanical approach. There are two micromechanical models, i.e. Generalized Method of Cell (GMC) and Square Fiber Model (SFM), were employed in this study. In addition, two different fiber arrangements, i.e., square edge packing and square diagonal packing as well as the fiber shapes, i.e. square type and round type, were taken into account. The finite element analysis with commercial code ANSYS was also adopted to investigate the fiber arrangement effect and the fiber shape effect. It was indicated basically, the mechanical behaviors were not affected appreciably by the fiber shape. On the contrary, the fiber arrangements play an essential role on the mechanical behaviors. The square edge packing demonstrates stiffer behaviors than the square diagonal packing. In order to verify the model predictions, off-axis graphite/epoxy composite specimens were tested at strain rate ranges from 10E-4/s to 550/s. Comparison of model predictions obtained from GMC and SFM analysis with the experimental results revealed that the micromechanical approaches are capable of predicting the nonlinear rate sensitivity of off-axis specimens although there are still distinctions between the model and the experimental results.